MY MATEX NOTES

In today´s post we will prove the following result by contour integration Click here to read the post.

In this entry we introduce the Arithmetic Geometric mean and show it´s connection with the complete elliptic integral of the first kind. This relation is one way to establish the connection between the Jacobi theta function and elliptic integral. and Click here to read the article. Important to note that in this entry we wont get into a detailed study of elliptic integral. Commentaries and feedbacks are welcome.

In this blog entry we will prove Ramanujan´s Psi Sum, namely Click here for the proof. As corollaries of the above formula we show that wich relies also on Jacobi triple product proved here :

In this post we will prove the following result Click here for the proof We have relied on the previous established result Proof   here .

In this entry we will solve the following integral to this end we should recall a previous established result. Click here for the proof of the integral.                       Proof of the binomial series here   .

In this entry we will prove the following result Click here to read it. Some previous established results were used, i.e.: Lerch´s formula Click here for the proof. Relation between Bernoulli´s polynomials and Hurwitz zeta function click here for the proof (equations 8.22 and 8.30)

This entry has some of the infinite product related to Jacobi Theta function proved. Click here to read it. The Jacobi triple product proved here , plays a central role in their proof as well some special values of the Jacobi theta function, see here

          Today we will prove this infinite series which involves the reciprocal of the central binomial coefficient squared, namely Click here for the proof.